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How about because it is simple, easy to remember & works well enough as a basic estimate for average conditions.

Rather like the "rule of twelfths" which I can use to estimate depths (for crossing sandbanks or using swatchways) in my head while steering & looking at a chart.

Or the 2hrs(etc) before/after HW guidelines for harbour entrances & bars given in pilot guides.

They suit me & work well for my purposes. I don't want to be running round trying to find the right graph for each situation to measure my chain to the last foot; especially when I work with 9-13m tidal ranges.

I don’t believe you have taken into account the dynamic loads.
The real world observations show that at the sort of wind strength likely to trouble a set anchor the chain entirely lifts off the bottom, with any practical chain length combinations. When the chain is essentially straight, the holding power is directly related to the angle of pull which is can be calculated from the scope ratio.
This is a simple model to a complex problem, but I believe it is more accurate than the model you propose.
.
The fundamental flaw is that you have assumed the weight of the rode is going to keep the pull at the anchor horizontal. If you dive on your anchor the next time there is a strong wind you will see this doesn’t happen.

Sorry to be negative. It looks like lots of work and it is still interesting and useful data.

Ages ago I did some work, for fun, on the shape of glider winch launch cables during the launch. It's a similar problem to the anchoring one: although the mass/length of the cable is a lot lower, there's a lot more length for things to happen in.

My conclusion was that simple static calculations (shape of cable vs position and pull at the glider end) were relatively straightforward but also fairly pointless, because the dynamic effects of surges and oscillations were just as important.

I'd expect exactly the same to be true of an anchor cable attached to a boat moving around in choppy conditions. there will be all sorts of waves and transients in the cable.

Originally Posted by richardabeattie

Put me out of my misery - are you saying that depth X 3 plus a bit for luck is too little or too much?

It's about right, and in conditions where it isn't you'll already have put enough out.

I'm more than happy with a 1:3 in somewhere like Puilladobhrain with little fetch, close neighbours and a sticky clay seabed (actually 1:3.2809 as I have my depth sounder that shows feet, so 10 feet depth == 10 metres anchor chain), however in sandy places I allow more chain, and in anchorages such as the Garvellachs where there can be a bit of swell and the bottom is mainly smooth rock then every bit of weight and friction helps.

1:3 is a reasonable rule of thumb, and a good starting point. It's a bit like the stopping distance tables on the back of the highway code, adjust to suit the conditions.

Put me out of my misery - are you saying that depth X 3 plus a bit for luck is too little or too much?

He is saying it is about right (depending on the size of your bit for luck).

I think this is an underestimate, for the reasons stated by noelex.

What I don't understand is the undercurrent of hostility to maths that pervades some of the posts. Without maths there would be no engineering (or navigation, for that matter) and our boats would lack much of what we have come to expect.

What I don't understand is the undercurrent of hostility to maths that pervades some of the posts. Without maths there would be no engineering (or navigation, for that matter) and our boats would lack much of what we have come to expect.

I'm not hostile to maths at all, myself. I do it for a living.

However, one of the most important things about maths is knowing how and when to apply it. Does anchoring need the degree of precision suggested by some folk (not just the OP)? I don't think it does. Three times depth is just fine for most situations: any fule kno that it's just a minimum, and whack some more out if needed.

..., because the dynamic effects of surges and oscillations were just as important.

I'd expect exactly the same to be true of an anchor cable attached to a boat moving around in choppy conditions. there will be all sorts of waves and transients in the cable.

You may be right, but I have a fetish for numbers and was seeking empirical data. When I have measured dynamic forces, and I give a means to do so in the document, as does the load-cell method Viv gave the URL for, I have found that they were really not that much bigger than the static, like 25% or 50% more, not 3x. This surprised the hell out of me, I was expecting greater. Maybe it's because I have a long keel, and a light boat might give biggger variation (but not necessarily bigger maxima). In any case, dynamic effects are hardly likely to lower the maximum pull, and the rules of thumb already suggest far too little chain in shallow water, which is possibly one reason that anchor tests have such poor reproducibility.

But, with respect, most posters have, I think, misunderstood my point: experienced sailors, which is pretty likely to include the vast majority of us on this forum, already do by instinct or experience what's right, so don't need my graphs except maybe for interest. I emphasised this in my first post. Of course I let out about 15m + 3x depth and then adjust a bit when in v deep or in v shallow or the wind is v strong, just like everyone else. Even I - a self confessed mathematican - am not solving differential equations everytime I go for a sail!

But havn't all of us got first hand experience of some boat, frequently a beginner, a mobo or French, dragging down onto us? The point I am trying to make is that the books and courses give a concrete rule which, once we've gained some experience, none of us actually obey. I'm trying to encapsulate in graphical form what we actually do. It would be easy to give this in classes and then discuss its limitations and how one can approximate it over the reduced range of circumstances we normally experience. We're not infants FFS and don't need the O level (ok GCSE) dumbed down version: tell it as it is, _then_ let us decide how we might simplify it in the light of our circumstances.

I think the OP has thrown some useful light on the subject. The RYA now teach x5 depth for chain which I think is not very useful. In our case, with 90m of chain that unnecessary limits us to less than 18m depth which I think fails to take account of what is happening in the catenary. If the forces are low I am confident that my 90m should get us much more than that. Haven't had to do it much in the recent past, however, in Cyprus and using previous boat once anchored in 35m and was very happy with 60m of chain cable during what was a very quiet night.

Once anchored in Poole harbour during a F8/9 in thick mud and only 3 to 4 m depth. Had the same 60m out and was surprised to see the chain cable becoming less and less vertical. We didn't drag and thanks to the critical angle graph I can now see that I could have slept a bit more soundly than I did at the time. As for snatch loads, they were quite great, dampened by a long snubber, but when I came to lift the anchor, in that mud, I found that the snatching had probably helped dig the anchor in as it was very difficult to break out.

So I'll be printing off a couple of graphs and using them as well as applying a safety fudge factor. Can't have too much information on which to select a course of action.

By the way, the expression "rule of thumb" comes from the law that a man could beat his wife with a stick so long as it was no thicker than his thumb. Thankfully that is one rule of thumb which is now defunct.